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Application of numerical inverse Laplace transform algorithms in fractional calculus. (English) Zbl 1210.65201

Summary: Laplace transform technique has been considered as an efficient way in solving differential equations with integer-order. But for differential equations with non-integer order, the Laplace transform technique works effectively only for relatively simple equations, because of the difficulties of calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the complicated fractional-order differential equations, we investigate the validity of applying numerical inverse Laplace transform algorithms in fractional calculus.
Three numerical inverse Laplace transform algorithms, named Invlap, Gavsteh and NILT, were tested using Laplace transforms of fractional-order equations. Based on the comparison between analytical results and numerical inverse Laplace transform algorithm results, the effectiveness and reliability of numerical inverse Laplace transform algorithms for fractional-order differential equations was confirmed.

MSC:

65R10 Numerical methods for integral transforms
44A10 Laplace transform
34A08 Fractional ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
65L05 Numerical methods for initial value problems involving ordinary differential equations
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